J. L. Steimke
Westinghouse Savannah River Company
Aiken, SC 29808

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An Excel spreadsheet calculation was previously used to model the HB-Line Phase II Eductor Systems [1]. Two eductors are used for Phase II processing. One is in the Column Line and is used to pump the contents of the Recycle Tanks to H Canyon. The other is in the Mechanical Line and is used to pump the contents of the Filtrate Tanks to H Canyon. The eductors serve the functions of both pumping and diluting product bearing solutions. Dilution must be reliably controlled because of criticality concerns with H Canyon Tanks. The previous calculation indicated dilution ratios of approximately 1.4 : 1. HB Line Engineering requires a dilution ratio of at least 4 : 1 and requested a calculation of an orifice plate that would give that dilution ratio when placed upstream of the suction side of the eductors. The orifice plates will be inserted between existing sets of flanges, 2235F for Recycle transfers and 2612F for Filtrate transfers. The calculated orifice size is 3/32". A conservative calculation of dilution factor showed that the dilution factor exceeded 4.16 : 1 for both systems when the eductant was 14 molar and the fluid being pumped was 0.35 molar. The dilution factor exceeded 4.91 : 1 for both systems when the eductant was water and the fluid being pumped was 0.35 molar.

It should be noted that inserting the 3/32" orifice plate in the line will generate low pressures upstream of the eductor which may induce flashing in the liquid being pumped. Flashing may cause erratic performance of the eductor or other problems such as increased rates of erosion or corrosion. Flashing is a conservatism with regard to dilution factor and if it occurs it will cause a dilution ratio larger than 4 : 1. A long term solution that avoids flashing is to replace the present ½" eductors with the next larger size, ¾". The reason that this change increases dilution factor is because a larger eductor consumes more eductant. An orifice plate would still be necessary. However, the hole size would be larger, suction pressures would be higher, and there would be no flashing.

The calculation of flows in the eductor systems was previously described [1]. Three changes were made in the calculation. First, equations were added to represent the pressure loss of the orifice plates. Second, a ½" eductor was performance tested in the Thermal Fluids Laboratory [2]. The resulting correlations were placed in the spreadsheet model, replacing correlations based on vendor supplied data. Third, the correlations for density and viscosity of nitric acid solutions were extended to 14 molar and those correlations were placed in the model.

Crane [3] gives the following equation for K factor for an orifice plate.

The K factor expresses the number of velocity heads of pressure loss, where one velocity head is equal to rv²/2, r is the density of the liquid and v is the velocity upstream of the orifice. The terms b and C are the ratio of orifice diameter to upstream diameter and the orifice discharge coefficient, respectively. A graph in Crane showed that C is equal to 0.59 for the range of Reynolds numbers and b of interest. The pressure drop represented by equation 1 is measured from a pressure tap one pipe diameter upstream of the orifice plate to a second pressure tap one-half pipe diameter downstream of the orifice plate. Further downstream there will be some pressure recovery. Blevins [4] gives a table of a, which is a measure of pressure recovery and is defined as the ratio of the permanent pressure loss to the pressure drop between the pressure taps described above. The Blevins table is reproduced below.

The following equation fits the data in the least squares sense.

Combining this information gives an equation for the permanent pressure loss from an orifice plate.

The performance of a ½" eductor was measured in the Thermal Fluids Laboratory [2]. The new correlation for pressure drop across the nozzle, DP_noz, in the ½" eductor follows where the units of pressure drop and flow of eductant, F_educ , are psid and gpm and S_educ is the specific gravity of eductant.

The term DP_noz is defined as the eductant supply pressure minus the suction pressure. The new correlation [2] for the pressure increase generated by the eductor follows.

The term DP_pump is defined as the eductor discharge pressure minus the suction pressure. The terms F_suc and S_suc are the flowrate and specific gravity of suction liquid, respectively.

Data for the density and viscosity of nitric acid solutions was taken from two sources [5, 6] that extended the range of data beyond 14 molar. The data are plotted in Figure 1 as a function of molarity, M. The following polynomial curve fits were determined. Density (r) has units of g/mL and viscosity (m) has units of centipoise.

The diameter of the orifice was determined using the following method. Both the existing model for the Recycle System and the existing model for the Filtrate System have an equation for the pressure drop in the suction line connecting either the Recycle Tank or the Filtrate Tank to the suction connection of the corresponding eductor. This equation had a term for miscellaneous losses in the piping such as for elbows. The term K_orif was added to that term. The most conservative molarities, 0.35 M for suction liquid and 14 M for eductant, were inserted in the model and the term K_orif was iterated to give a dilution ratio of 4 : 1. Then equations 1 and 2 were used to evaluate b. Multiplying b by the inside diameter of the ½" tubing gives the diameter of the orifice. The results were nearly identical for the Recycle System and the Filtrate System. An orifice with a diameter of 3/32" always gave a dilution ratio of more than 4 : 1. Calculations for Recycle transfers and Filtrate transfers are listed in Attachments 1 and 2. A summary of the results appears below.

Three conservatisms were employed to create a dilution ratio that is larger than 4 : 1 in actual practice. First, the orifice was sized using the combination of molarities for the suction fluid and the eductant that gives the smallest dilution ratio. Second, there has been evidence for a leak of eductant around the eductor. The evidence for a leak of eductant is shown in Figure 2, which plots dilution ratio for actual Phase II transfers. For Recycle transfers up to transfer #27 the average dilution ratio was 5 : 1. On February 15, 2001 a valve suspected of leaking eductant, 2683HV, was blanked to exclude the possibility of leakage. Figure 2 shows that dilution ratio changed to 4 : 1. The points marked new eductor were taken after the old eductor was replaced with the eductor that had been performance tested in the TFL [2]. The hardware difference between the old and new eductor has not been determined. Further evidence of a leak of eductant is noted on Figure 2. The calculated dilution factor for both Recycle and Filtrate transfer is 1.4 : 1. The measured dilution ratios for Filtrate transfers or for Recycle transfers with the new eductor were close to 2 : 1. The discrepancy between the calculated and measured dilution ratios is consistent with a leak of eductant. The third conservatism notes the fact that the use of the orifice plate creates a significant partial vacuum at the suction of the eductor. The calculated partial vacuum is as much as –13.2 psig or 1.5 psia. The largest partial vacuum used for the TFL performance tests or the vendor performance tests was less, –8.8 psig. A partial vacuum of –13.2 psig may induce flashing at the suction inlet of the eductor. Flashing would diminish the ability of the eductor to pump liquid, without decreasing the consumption of eductant. Therefore, flashing would increase the dilution ratio.

1. In the short term, install 3/32" orifice plates in the suction line of both the Recycle eductor and the Filtrate eductor. This will increase the dilution ratio to more than 4 : 1.
2. Check for an eductant leak by blanking valve 2683HV for Recycle transfers or blanking valve 2684HV for Filtrate transfers. If there is a leak, the dilution ratio will decrease.
3. Replace the present ½" eductors with ¾" eductors. These eductors could be used to achieve the desired 4 : 1 dilution ratio with no risk of flashing.

1. J. L. Steimke, "Calculation of Flows for HB Line Phase II Eductor Systems", WSRC-TR-2001-00014, January 31, 2001.
2. J. L. Steimke, "Eductor Performance Testing", WSRC-TR-2001-00229, May 7, 2001
3. Crane Co., Flow of Fluids Through Valves, Fittings and Pipe, Technical Paper No. 410, 1988.
4. Robert D. Blevins, Applied Fluid Dynamics Handbook, 1984.
5. Robert H. Perry, Cecil H. Chilton and Sidney D. Kirkpatrick, Chemical Engineers’ Handbook, Fourth Edition, 1984.
6. Kirk-Othmer, Encyclopedia of Chemical Technology, Fourth Edition.
   
   
   
   

Attachment 1

Attachment 1

Attachment 2

Attachment 2